@kali it isn't because she hates him or something. When the duke went after the princess to rescue her, he almost lost his life. Roselia feels that if she continues to stay with him, the duke's life will be in danger always. That's why she's using the princess as an excuse to fend off the duke. Roselia's giving the duke an excuse that he chose the princess over her and that she 'hates' him. She's deliberately giving off that excuse. She can't just walk up to him and say "Oh, duke, you'll die if you stay with me. That's why I'm going. Bye bye."
And as for the duke pursuing Roselia, it's like a boyfriend coaxing and making up to his girlfriend. He's only pushing a bit because he knows she still loves him and wants to put in the effort. Roselia is only getting angry because her efforts to keep the duke away from her are failing. She's not angry with him. She's afraid that the longer the duke stays near her, the more in danger he'll get. That's why she's reacting like that so that the duke will finally give up on her and go back.